1. Field of the Invention
The invention relates to control systems directed by digital computers, and more particularly to a control system for use in connection with a physical system. The physical system responds to an input stimulus by generating an undesired output which affects a physical body, in addition to its desired outputs. The distributed control system generates a state-space model of the transfer function between stimulus and undesired output and, using optimizing procedures which use a set of optimal control gains, generates a derived output from that space-state model which approximates the undesired output for a given stimulus. The control system then supplies the derived output to a transducer which applies a transducer output to the physical body to cancel the undesired output.
2. Description of the Prior Art
A number of modeling procedures have been developed in the prior art to control the dynamics of a continuous distributed-parameter system in convenient forms. These include a first-order system of partial differential or difference equations method proposed by Wang and Tung in 1964, in a paper entitled "Optimum Control of Distributed-parameter Systems", in Journal of Basic Engineering, Trans. ASME, pages 67-78; a separation method proposed by Meirovitch in 1967 in a book entitled "Analytical Methods in Vibrations (New York: The Macmillan Co.), and by Meirovitch and Silverberg in 1983 in a paper entitled "Globally Optimal Control of Self-adjoint Distributed Systems", in Optimal Control Applications and Methods, Vol. 4, pages 365-386; and a multidimensional state-space method proposed in various forms by Attasi in 1973 in a paper entitled "Systems Linearies Homogenes a Deux Indices", in IRIA Rapport Laboria, No. 31; by Roesser in 1975 in a paper entitled "A Discrete Space-State Model for Linear Image Processing", in IEEE Transactions on Automatic Control, Vol. AC-20, No. 1, pages 1-10; by Fornasini and Marchesini in 1978 in a paper entitled "Doubly-Indexed Dynamical Systems: State-space Models and Structural Properties", in Math. Systems Theory, pages 59-72; and by Kaczorek in 1985, in a book entitled Two-dimensional Linear Systems (Heidelberg, Germany: Springer-Verlag). I have also done work in this area in my doctoral thesis, made publicly available less than a year prior to the filing date of this application, entitled Multidimensional Discrete State-space Modeling Optimal Control and Tracking of The Linear Distributed-parameter Systems, D.Sc. Dissertation, School of Engineering and Applied Science, George Washington University, Washington, D.C.
This application discloses a control system for controlling the dynamics of a distributed-parameter system in an optimum manner. Many researchers have developed techniques to manipulate the dynamic characteristics of the distributed-parameter systems. These include Wang and Tung in the work cited above; Paraskevopoulos in 1979, in an article entitled Eigenvalues Assignment of Linear Multivariable Two-dimensional Systems, in Proceedings of the IEEE, Vol. 126, pages 1204-1208; Paraskevopoulos and Kosmidou in 1981, in an article entitled Eigenvalue Assignment of Two-dimensional Systems Using PID Controllers", in International Journal of Systems Science, Vol. 12, No. 4, pages 407-422, and Tzafestas and Pimenides in 1983, in a paper entitled "Feedback Characteristic Polynomial Controller Design of 3-D Systems in State-space", from the Control System Laboratory, School of Engineering, University of Patras, Patras, Greece, Vol. 314, No. 3, pages 169-189. Paraskevopoulos et al presented a method to reassign the poles of a two-dimensional system to a set of desired values using a static state-feedback or static output feedback controller, Paraskevopoulos et al developed a multidimensional proportional, integral, derivative (PID) controller for controlling the poles of the system, and Tzafestas et al extended the concept of poles assignment by feedback controllers to the three-dimensional systems. The difficulty associated with the implementation of these methods is in knowing or determining the poles and the eigenvalues of the state-space model of the distributed-parameter system.
The prior art includes an optimal control technique as illustrated by Sage and White, in 1977, in a book entitled Optimum Systems Control (New Jersey: Prentice-Hall Inc.), and by Kou in 1980, in a book entitled Digital Control Systems (New York: Holt, Rinehart and Winston Inc.).